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Abstract: We establish a general hierarchy theorem for quantifier classes in the infinitary logic L ! 1! on finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure. This implies the solution of several open problems in finite model theory: On finite structures, positive transitive closure logic is not closed under negation. More generally the hierarchy defined by interleaving negation and... (Update)
Context of citations to this paper: More
...larger quantifiers and mimics LTH more closely. Results of Gradel and McColm, showing that a quantifier defined hierarchy within NL is proper [27], give us hope of showing that SBH (QL) does not collapse. Their classes are defined by alternations of 9 and 8 quantifiers, which...
...quantifiers and mimics LTH more closely. Results of Gradel and McColm, showing that a quantifier defined hierarchy within NL is proper [26], give us hope of showing that the SBH (QL) does not collapse. Their classes are defined by alternations of 9 and 8 quantifiers, which...
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BibTeX entry: (Update)
E. Gradel and G.L. McColm, "Hierarchies in transitive-closure logic, stratified Datalog, and infinitary logic," Ann. Pure Appl. Logic 77 (1996) 169--199. http://citeseer.ist.psu.edu/387784.html More
@misc{ gradel96hierarchies,
author = "E. Gradel and G. McColm",
title = "Hierarchies in transitive-closure logic, stratified Datalog, and infinitary
logic",
text = "E. Gradel and G.L. McColm, Hierarchies in transitive-closure logic, stratified
Datalog, and infinitary logic, Ann. Pure Appl. Logic 77 (1996) 169--199.",
year = "1996",
url = "citeseer.ist.psu.edu/387784.html" }
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